There could be little President Barack Obama can do to find common ground with Paul D. Ryan, given their deep ideological differences and House conservatives’ inevitable demands for the speaker-in-waiting.

With Ryan's announcement that he will seek the speakership, all eyes now turn to the Wisconsin Republican's ability to manage his fractious caucus and find just enough common ground with a president many conservatives revile. Ryan will have little time to settle in because of some fast-approaching fiscal deadlines. Congressional leaders must find a way in coming weeks to avoid a potentially catastrophic debt default, then see if they can strike a long-term budget deal.

But it is unclear how Obama and Ryan will resolve fundamental differences, including defense and domestic spending caps. House Republicans want any year-end budget deal to boost defense spending; the president is holding firm that he will only sign such a plan if it includes an equal domestic spending hike.

“The Ryan-Murray [budget] compromise did allow spending in excess of what would have been permitted on both fronts,” said William A. Galston, a former administration official for President Bill Clinton, now at the Brookings Institution. “Is Congressman Ryan prepared to accept, however grudgingly, the terms of spending symmetry?

“I don’t think the president will go along with asymmetry and demonstrated that with his veto," Galston added, referencing a Pentagon policy bill that authorized $38 billion in additional fiscal 2016 Pentagon spending.

Some GOP lawmakers believe such moves are illustrative of a White House unwilling to compromise. House Natural Resources Chairman Rob Bishop, R-Utah, says Ryan faces an uphill climb.

“The question should be,” Bishop said in a brief interview, “Can anyone work with this White House?”

At the White House, the message about Ryan’s likely speakership and a new era of Obama-congressional dealmaking is measured.

Press Secretary Josh Earnest told reporters last week Obama has been “quite clear that he respects Paul Ryan” as someone “who obviously has spent a lot of time seriously thinking about some of the significant challenges facing the country.”

But Earnest's remarks also made clear the president and the presumptive House leader are members of different political parties with many divergent views. And that means a long-term budget deal — and future accords — won’t be guaranteed.

“At the same time, the president has profound and occasionally vigorous disagreements with him on fiscal issues and presumably other things too,” Earnest said.

The well of Ryan-Obama legislative partnerships is shallow.

Many lawmakers and experts point to the budget deal Ryan struck with Sen. Patty Murray, D-Wash., in 2013 as an example of his ability to work with Obama. While he didn’t negotiate that plan directly with the president, Obama blessed it and signed it into law.

Several lawmakers, Republican and Democratic, also pointed to efforts Ryan attempted on an immigration overhaul in 2013 and a trade package Obama pushed through earlier this year as examples of cases in which the two have worked together.

On the trade legislation, Deputy House GOP Whip Tom Cole of Oklahoma said “not only did [Ryan] do it, he did that after being an opponent of the president — I thought it spoke highly of both of them, particularly Paul.”

Cole told CQ Roll Call he believes Ryan and Obama “respect each other intellectually. ... These are two very bright people.”

Still, Cole cautions against expecting drastic changes in the congressional GOP-Obama relationship under a Speaker Ryan.

“But I also think, boy, the philosophical chasm is great,” he added. “And, yeah, that could be a problem.”

Even senior Democrats are hailing the speaker-in-waiting as having the kind of get-things-done makeup and deal-minded approach to find some common ground with Obama and their caucus.

“I think he’s smart enough to know what he needs to do, and it sounds to me like he’s trying to ensure … he can get some things done,” Becerra told reporters.

But just how much he and Obama can get done, Galston said, depends on whether the two are willing to budge on policy and spending issues. And that, he said, depends on their willingness to “say no to the people they respectively answer to.”

“I would think, for instance, that the president and Mr. Ryan ought to be able to reach agreement on a transportation bill,” he said. “Now, it may require each one to swallow hard."